Adjectives: A Uniform Semantic Approach - University of Windsor

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Adjectives: A Uniform Semantic Approach 337 Jane is an [attractive [blond woman]] (8) And, the set-theoretic representation of the adjectival phrase might look something like: Attractive ∩ (Blond ∩Woman) (9) However, this representation does not capture the intended meaning. That is, attractive in (8) modifies the expression blond woman as a whole. In other words, for someone who utters (8), blond is essential to the extent that if the denotation of Jane were not blond, the utterance (8) might not have taken place. 3.3.2 A Solution In order to accommodate adjective phrases, we need to do two things. First, expand our ontology to include properties—assuming that adjectives denote properties. This will enable us to form new property types from the more basic ones. Second, we need a rigorous typing system, whereby every set has a type. The typing system we are proposing shortly will enable us to generate new types from the basic ones. The type system must correspond to the grammar’s production rules. Grammar rules for adjective phrases might look like the following: AP ::= AN N::= AN | man |woman |man |dancer| surgeon|… A::= good | red |attractive| fragrant|… The rules in (10) will recursively generate adjective phrases such as good man, fragrant red roses, etc. The grammar in (10) generates noun phrases by means of a string concatenation function. A typing system should parallel the grammar and be able to recursively define new types from existing ones. Such a system is inductively defined as follows: a) The basic types are the nodes of the taxonomy of Figure 1, e.g. Nat(ural) Kind, Kind, Properties, Role, Implement, and ┬. b) If a is a property type and b is a basic type, then a: b is a type, see the example regarding the wide-scope reading. c) If a and b are property types then a-b is a property type, see the example regarding the narrow-scope reading. d) If a is a type and b is a non-property type, then a: b is a type. e) Nothing else is a type. (11-a) states the basic types assumed. In a full-fledged system, the set of admissible basic types must be larger than this. However, this set suffices to demonstrate our approach. (11-b) states that the first basic type of a resulting set is a property type. This is because here we are only treating adjective-noun—not noun-noun—combinations, for example. (11-c) generates property types. This is necessary for dealing with narrowscope readings, i.e. when an adjective modifies another adjective and both modify a noun or an adjective phrase. Both (11-b) and (11-d) ensure that the resulting type is that of the head noun. (10) (11)
338 N. Abdullah and R.A. Frost Fig. 1. A taxonomy with properties With the typing rules of (11) in mind, the representation of the adjective phrase in (8) is as follows, || Jane|| = j: Blond = {j: T,…}: blond Woman = {j: woman,…}:woman Blond ∩ Woman = {j: blond: woman, …}: blond: woman Attractive = {j: blond: woman, …}: attractive Attractive ∩(Blond∩Woman)={j:attractive:blond:woman}: attractive:blond: woman The syntactic-semantic steps that led to the above representation are shown below. Fig. 2. Wide-scope reading of Jane is an attractive blond woman It should be noticed that from reading (8) the following can be deduced: Jane is blond Jane is a woman But not necessarily, Jane is attractive
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Adjectives: A Uniform Semantic Approach - University of Windsor

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